INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2010; 84:379–433 Published online 23 April 2010 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/nme.2898 Post buckling analysis of shear deformable shallow shells by the boundary element method P. M. Baiz ∗, † and M. H. Aliabadi Imperial College London, South Kensington, London SW7 2AZ, U.K. SUMMARY This paper presents four boundary element formulations for post buckling analysis of shear deformable shallow shells. The main differences between the formulations rely on the way non-linear terms are treated and on the number of degrees of freedom in the domain. Boundary integral equations are obtained by coupling boundary element formulation of shear deformable plate and two-dimensional plane stress elasticity. Four different sets of non-linear integral equations are presented. Some domain integrals are treated directly with domain discretization whereas others are dealt indirectly with the dual reciprocity method. Each set of non-linear boundary integral equations are solved using an incremental approach, where loads and prescribed boundary conditions are applied in small but finite increments. The resulting systems of equations are solved using a purely incremental technique and the Newton–Raphson technique with the Arc length method. Finally, the effect of imperfections (obtained from a linear buckling analysis) on the post-buckling behaviour of axially compressed shallow shells is investigated. Results of several benchmark examples are compared with the published work and good agreement is obtained. Copyright 2010 John Wiley & Sons, Ltd. Received 12 March 2009; Revised 9 February 2010; Accepted 14 February 2010 KEY WORDS: shallow shells; post buckling; shear deformable theory; boundary element method 1. INTRODUCTION Maintenance of stability is vital in the design of thin-walled structures. Physically, loss of stability means that the structure is unable to sustain a small increment in load by a small increment in configuration: because either some motion takes place and, by virtue of damping, the structure eventually assumes a new, relatively distant equilibrium configuration, or else there is sudden motion leading to catastrophic failure. ∗ Correspondence to: P. M. Baiz, Imperial College London, South Kensington, London SW7 2AZ, U.K. † E-mail: p.m.baiz@imperial.ac.uk Contract/grant sponsor: Imperial College London Copyright 2010 John Wiley & Sons, Ltd.